Abstract

The reconfigurable mesh (R-Mesh) has drawn much interest in recent years, due in part to its ability to admit extremely fast algorithms for a large number of problems. For these algorithms to be useful in practice, the R-Mesh must be scalable; that is, any algorithm designed for a large R-Mesh should be able to run on a smaller R-Mesh without significant loss of efficiency. This amounts to designing a ‘scaling simulation” that simulates an arbitrary step of an N×N R-Mesh on a smaller P×P R-Mesh in O(N2/P2f(N, P)) steps; f(N,P) is a nondecreasing function representing the simulation overhead. The aim is to minimize this overhead, ideally to a constant.

In this paper, we present a scaling simulation for the general (unconstrained) R-Mesh. This simulation has an overhead of log N (smaller than the log PlogN/P overhead of the previous fastest scaling simulation), using a CREW LRN-Mesh (a weaker version of the General R-Mesh) as the simulating model; prior simulations needed concurrent write.